You really might want to give us a lot more context on what you're doing. What is z? What is [itex]z_{max}[/itex]? If you tell us what the problem is, we can even tell you if the acceleration is constant.

It is from a book on how to slow atoms with a Zeeman slower. Here [itex]z[/itex] is the coordinate (longitudinal, along the magnetic field), and [itex]z_{max}[/itex] I believe is the longitudinal coordinate, where the velocity is zero. Sorry, I should have stated that at first.